


Zeno's Paradox of Brothers on a Hotel Bed

by elmathelas



Category: Supernatural
Genre: Alternate Universe - Apocalypse, M/M
Language: English
Status: Completed
Published: 2012-08-22
Updated: 2012-08-22
Packaged: 2017-11-12 16:43:39
Rating: Teen And Up Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 1,517
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/493457
Author URL: https://archiveofourown.org/users/elmathelas/pseuds/elmathelas
Summary: <blockquote class="userstuff">
              <p>It's the end of the world.  Dean lies on a hotel bed next to Sam, and thinks about the paradox of the turtle.</p>
            </blockquote>





	Zeno's Paradox of Brothers on a Hotel Bed

**Author's Note:**

> Contains allusions to "Brothers On A Hotel Bed" by Death Cab for Cutie, "Zeno's Paradox of the Tortoise," by Plato, "The Road Not Taken" by Robert Frost, "Thirteen Ways of Looking at a Blackbird," by Wallace Stevens, and, upon reflection, owes a debt to "When We Went to See the End of the World, by Dawnie Morningside, age 11 and 1/4," by Neil Gaiman.

Dean had always been good at math. Teachers had always seemed surprised, but it was simple. Math didn't change from school to school, and there was no room for argument. He might have been removed from seventh grade English for suggesting that Frost's _The Road Not Taken_ could be interpreted as meaning that all choices are bullshit and life is meaningless anyway, but the circumference of a circle was always Pi multiplied by diameter, and that was that. Sam had struggled with math, and really, it wasn't surprising. For Sam, there were thirteen ways of looking at anything.

Dean only struggled with the theoretical side of math. Two lines that appear parallel to the naked eye but have differing rises may take miles to intersect, but no matter how slow the approach to that moment, they will only intersect at one point. That point has no mass, no volume, does not exist other than as the place where those two lines cross. The concept offends his mind. On two-lane blacktops he watches the double yellow line down the middle, thinks about them traveling out over miles and miles. If there's an imperfection, if they're not truly parallel, when they finally cross it will be because they got closer and closer, gelled together like two pieces of skin healing over a wound. There's no way they cross at only one point, there's no way that they don't occupy the same space for more than that insignificant, almost imaginary moment, and yet part of his mind knows it must be true.

He's good at figuring. The ceiling above his head, for example. Given a few moments of concentration, he could estimate how many dents are in the acoustic tile for the room, for this floor, the hotel. Given enough thought he could make a decent guess as to how many dents in acoustic tile there are in the entire state, though he'd lapse into conjecture based on population, office parks, schools, cheap apartment buildings and dormitories and motels, the kinds of places that have acoustic tile hanging ceilings instead of plaster, and a gross estimate of how many of them are still standing. He wouldn't count the tiles that have been turned to chunks of rubble. Given enough time he could work up a rough estimate too for how many people are left in the United States, and whether or not it would make a dent in the population of the world, really. They kept calling it the end of the world, the battle for the preservation or the destruction of all of the earth, but it seemed to have been waged mainly in the US. He viciously squashes down the part of his mind that sneers _how appropriate._ That's a thought worthy of Sam, and he takes a moment to check to see if he has the brainpower to come up with a reply, for when Sam inevitably trots out that line, but he's got nothing.

Sam's breathing matches his, even now that Dean's awake. It was off by a beat a little while ago, just out of time, a jarring syncopation that set his teeth on edge. He can appreciate that sort of thing, in, say, Enter Sandman, but when it's a noise being made by your brother, or your car, well, it goes from introducing a heady sort of melodic tension to being just plain annoying. Either he or Sam adjusted, though, and they match now. He tries not to think too hard about it, because then they'll get out of sync again. His brain is hungry for something to think about. His eyes have been staring up at the tiles for so long that the image has whited out and blurred around the edges. He's past the urge to blink.

He thinks about leaning his head on the driver's side window in the back seat of the car, feet resting against the back of Dad's seat but so steady and still as to be just a constant pressure, no reason for Dad to grumble about him kicking the seat. On the opposite side of the car Sam is kicking the passenger seat, slowly, so slowly that for a moment every few seconds Dean thinks he's stopped, and then it starts again and he wants to scream but instead he looks down at the yellow lines. Here, his perspective makes it look like the top line is smaller, squished, the bumps of gravel and dirt in the lower line moving along more quickly because they're closer. If he lets his eyes relax then suddenly it's the road that is moving, not them. The car is holding still and the road is whipping along underneath them, turning the wheels. He feels carsick, turns his head to look at Sam, maybe snap at him to stop kicking the goddamn seat.

Sam's got the thumb and forefinger of his right hand making a semi-circle against his jeans, the index finger of his left hand tracing a path from one side to the other in a strange pattern. For a weightless, crazy moment Dean thinks Sam is working some kind of spell, drawing in the weft of the fabric, but that's absurd. Still, he asks.

"What are you doing, Sammy?"

Sam looks up at him, scowls, an odd look on his face.

"I'm thinking about the turtle."

Dean sighs. It's a typical Sam trick, introduce a subject just odd enough that the other party has to ask, _what turtle._ It's not fair, it's manipulative, but he falls for it every time.

"What turtle?"

"If there's a turtle in the bottom of a swimming pool, and he's standing at one edge," Sam puts his left index finger on the web between his right index finger and thumb. "He can walk halfway across." He moves his finger to the center of the circle. "Then halfway across the half."

"A quarter," Dean automatically supplies.

"Duh." Sam moves his finger again. "Then an eighth of the way, then a sixteenth, then a thirtysecond." His fingernail is nearly touching the opposite side. "He is always allowed to cover half the distance left but he'll never get there. But he has to."

"Why does he have to?" Dean asks. His math teacher two years ago had put this problem to them-- Zeno's paradox of the tortoise. It's a paradox because when you're walking anywhere you always have to cover half the distance first, then half of what's left, and so on, but in real life, you get there eventually. In real life, there's no capricious god telling the tortoise he can only move in increments of half of what remains.

"Eventually half of what is left is practically nothing," Sam says. "He'll just get so close he'll touch the wall."

"Practically nothing isn't nothing, though," Dean points out.

"That's what my teacher said." Sam slumps against the back of the seat.

"It's just a paradox," Dean says, "any time you go someplace you have to cover half the distance, and then half of what's left, and half of what's left after that until you're done."

Sam sits up and looks out the windshield, the blacktop illuminated by the Impala's headlights, but no further, two gray stripes against the black background, like they're driving into a void. For one moment Dean gets the feeling that he can see inside his brother's mind, see what he's seeing. It's them, halfway to their goal, then half again, then half again, until they're almost there, so close they can feel it in the way the air changes around them, but never there, suspended in time, almost done, but never quite. He shivers.

On the hotel bed he shivers at the memory and blinks, his vision blurring as his eyes release a film of tears to moisten his dry corneas. His hand shifts against the rough surface of the comforter, twitches, almost. There's something different. Sam's breathing hasn't changed, but something has, and when Dean picks up his head to look down he can see that Sam's hand is traveling towards his, in infinitesimally small increments, not inching closer, not even millimetering closer. He thinks for a moment, realizes that they haven't touched, not once, since the end of the world began. 

It's not over, the end of the world. It was half over, once, then half of what was left was over, and half again. Now the end of the world is splitting distances the size of atoms, moving towards its ultimate ending, absolutely appearing to stand still. It appears to have stopped but it hasn't, it's just suspended in a chain of fractions where the denominator is getting bigger and bigger; the numbers, if they were written out, would stretch for miles.

Dean hears the scratch of Sam's skin against the shiny surface of the comforter. He can't move as slowly as he thinks. Dean sighs, breaking the rhythm of their breaths, and moves, his hand crossing whole inches before it collides with Sam's, skin pressing into skin, sharing space as he clutches Sam's hand tightly in his own.


End file.
